In particular, when o=0, this yields the definition of a Lyapunov function Finding, for a given supply rate, a valid storage function(or at least proving that one exists)is a major challenge in constructive analysis of nonlinear systems. The most com-

with x(0)=I exist and are unique on the time interval t E [ 0, 1] for allTER\.Then discrete time system(4. 1)with f(5)=r(, i)describes the evolution of continuous time system(4.)at discrete time samples. In particular, if a is continuous then so is f Let us call a point in the closure of X locally attractive for system(4. 1)if there exists

Definition A real-valued function V: X H R defined on state space X of a system with behavior set B and state r:B×[0,∞)→ X is called a Lyapunov function if tHv(t)=v(a(t))=v(a(z(), t)) is a non-increasing function of time for every z E B according to this definition, Lyapunov

3.1.2 A general uniqueness theorem The key issue for uniqueness of solutions turns out to be the maximal slope of a=a(a) to guarantee uniqueness on time interval T=[to, t,, it is sufficient to require existence of a constant M such that

he variable t is usually referred to as the\time Note the use of an integral form in the formal definition(2.2): it assumes that the function tHa(a(t), t)is integrable on T, but does not require =a(t)to be differentiable at any particular point, which turns out to be convenient for working with discontinuous

Lecture 1: Input/Output and State-Space Models This lecture presents some basic definitions and simple examples on nonlinear dynam

ARGOS Overview Angular Resolution at 2=550 nm: 5 arcsec Wavelength Regime 400-700 nm FOr (Field-of-Regard): 120(full cone)

Introduction Objective: To compare the different imaging configurations for a Separated Spacecraft Interferometer operating from an Earths orbit

Goal: Give necessary optics background to tackle a space mission, which includes an optical payload Light .Interaction of light w/environment o Optical design fundamentals Optical performance considerations .Telescope types and CCd design interferometer types

Electromagnetic Formation Flight NRO DI Final review Friday, August 29, 2003 National reconnaissance office Headquarters Chantilly, VA LOCKHEED MART Massachusetts Institute of Lockheed Martin Corporation